Question

$| - 3 m |$
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Answer 1

The value |-3m| depends upon the value of m

Case 1: When m is a positive real number.

Since m is positive and it is multiplied with a negative number i.e., -3, it will give negative result.

Hence the modulus will open with a negative sign so that the output must be positive.

Thus, |-3m| = -(-3m) = 3m

Case 2: When m is a negative real number.

Since m is negative and it is multiplied with another negative integer, it will yield a positive real number.

Hence, the modulus will open with a positive sign so that the output is positive.

Thus, |-3m| = -3m

Conclusion:

• |-3m| = 3m ; m belongs to R+
• |-3m| = -3m ; m belongs to R-